How to get more points on a mesh (edit mode)?
In the comments I made, I probably misinterpreted the question. I never actually considered that you may be trying to use CtrlR on just the rim of the circle, and I thought you were trying to get more points on the surface of a filled circle.

The easiest way the get more vertices on the rim of a circle, is specifying the number of vertices when you add it. This is done in the Toolshelf right after adding the circle. If you do not see the toolshelf, make it visible by pressing T.



To add more vertices to an already created circle (or any object), you can subdivide it. In Edit mode there's a Subdivide button in the Toolshelf.



You may want to increase the Smoothness parameter. It's set to 0.000 by default, and this will make straight cuts. Setting it to 1.000 will make smoother cuts.